To determine how much yarn Kate had left over, we need to subtract the total length of yarn she used from the amount she initially bought.
Kate needed 3 pieces of purple yarn, and each piece had to be 4/5 meters. So, the total length of yarn she used is:
3 pieces * 4/5 meters per piece = 12/5 meters
Kate initially bought 5 meters of yarn. To find out how much yarn she had left over, we subtract the length of yarn she used from the amount she bought:
5 meters - 12/5 meters = (25/5 meters) - (12/5 meters) = 13/5 meters
Therefore, Kate had 13/5 meters of yarn left over.